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中央研究院物理研究所 高中物理科學培育計畫 電磁學 主要觀念的演進 Evolution of Concepts. 任慶運 東吳大學物理學系. 電磁理論所需的高等數學. 多變數向量函數 多重積分 偏微分方程式. 兩種表述方式：. 概念陳述 數學表式. 第一分 概念陳述. Track One Conceptual Development. 從「瞬時隔空作用」到「場」 法拉第 M. Faraday from “action-at-a-distance” to “field” 從「電」「磁」到「電磁」 厄斯特 H. C. Ö rsted
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中央研究院物理研究所高中物理科學培育計畫電磁學主要觀念的演進Evolution of Concepts 任慶運 東吳大學物理學系
電磁理論所需的高等數學 • 多變數向量函數 • 多重積分 • 偏微分方程式
兩種表述方式： 概念陳述 數學表式
第一分 概念陳述 Track One Conceptual Development
從「瞬時隔空作用」到「場」 法拉第 M. Faraday from “action-at-a-distance” to “field” 從「電」「磁」到「電磁」 厄斯特H. C. Örsted from “electricity and magnetism’’ to “electromagnetism” 從「光」到「電磁波」 馬克斯威 J. C. Maxwell from “light” to “electromagnetic wave” 從「以太說」到「相對論」 愛因斯坦 A. Eistein from “ether theory” to “relativity”
牛頓（Newton）：萬有重力（引力） 重力： • 庫倫（Coulomb）：電力、磁力 庫倫力： 平方反比律 inverse-square law
關於譯名 gravitaty應譯為「重力」而非「引力」 互相吸引是重力的屬性 庫倫力則兼有吸引與排斥兩種屬性 若以屬性命名，庫倫力豈不成為「引斥力」
科學方法 演繹法（外籀術）deduction 歸納法（內籀術）induction 觀測（observation） 天文 實驗（experiment） 物理 考察（investigation） 生物
重力的平方反比律 • Tycho Brahe 第谷 觀測 • Johannes Kepler 刻卜勒 行星運動三定律 • Issac Newton 牛頓 萬有重力：平方反比定律
The electric force is about a billion-billion-billion-billiontimes stronger than gravitation. 109 × 109 × 109 × 109 = 1036 庫倫電力約為萬有重力的一兆兆兆倍 （萬萬曰億，萬億約兆） 104 108 1012 「黃帝為法，數有十等。」 「十等者，億、兆、京、垓、秭、壤、溝、澗、正、載。」
大小怎麼比？ 估計數量級 estimating order of magnitude
比較兩個粒子的重力與庫倫力： 重力： 庫倫力：
Fe/ Fg = k q2/Gm2 以氦原子核（即 粒子）為例 m = 6.6 × 10-27 kg q = 3.2 × 10-19 C k = 9.0 × 109 C m2 N/C2 G = 6.7 × 10-11 m2 N/kg2 Fe/ Fg =9.0 × 109×(3.2 × 10-19) 2 /6.7 × 10-11×(6.6 × 10-27) 2 只數次方(數量級 ) = 10 1＋9 ＋1－38 －1 ＋11 －2 ＋54 = 1035
重力極其微弱， 故用巨大天體。 • 庫倫電力雖甚大於萬有重力， 仍須使用精密儀器仔細測量。
扭秤（torsion balance） • J. Michell 發明 測量小質點間重力 • H. Cavendish 利用 測量小質點間重力 • C. A. Coulomb 發明 測量電力與磁力 Maxwell, Treatise,Art. 38 and 215
electric forcebetween two charges Q1and Q2 separated by a distance raction-at-a-distance瞬時隔空作用
名詞翻譯action-at-a-distance • 超距作用（物理學名詞第二次增訂本） • 瞬間作用（劉源俊） • 隔空抓藥（新聞詞彙） • 隔空力 • 隔空瞬時力 • 瞬時隔空力 瞬時隔空作用
對瞬時隔空作用的檢討 Although Newton had expressed doubt about the idea of action at a distance, most subsequent physics, as well as Newton’s, was based on that idea. Emilio Segrè
對瞬時隔空作用的檢討 Before Faraday, electric and magnetic, as well as gravitational, forces were usually considered as acting across space, separating the interacting objects. To his simple mind, however, such an “action in distance” did not seem to make physical sense, and seeing a load being moved from place to place he wanted also to see a rope which drags it or a stick with which it is being pushed. George Gamow
關於法拉第 數學知識不足 lack of formal mathematical knowledge 十九世紀最了不起的實驗物理學家 the greatest experimental physicist of the nineteenth century
馬克斯威的說法 關於法拉第 It was perhaps for the advantage of science that Faraday, though thoroughly conscious of the fundamental forms of space, time, and force, was not a professed mathematician. He was not tempted to enter into the many interesting researches in pure mathematics which his discoveries would have suggested if they had been exhibited in a mathematical form, and he did not feel called upon either to force his results into a shape acceptable to the mathematical taste of the time, or to express them in a form which mathematicians might attack. He was thus left at leisure to do his proper work, to coordinate his ideas with his facts, and to express them in natural untechnical language. Treatise, Art. 528.
It was perhaps for the advantage of science that Faraday, though thoroughly conscious of the fundamental forms of space, time, and force, was not a professed mathematician. 馬克斯威的說法 Treatise, Art. 528. 關於法拉第
He was not tempted to enter into the many interesting researches in pure mathematics which his discoveries would have suggested if they had been exhibited in a mathematical form, 馬克斯威的說法 Treatise, Art. 528. 關於法拉第 （馬克斯威屬於這一類）
and he did not feel called upon either to force his results into a shape acceptable to the mathematical taste of the time, 馬克斯威的說法 Treatise, Art. 528. 關於法拉第
or to express them in a form which mathematicians might attack. 馬克斯威的說法 Treatise, Art. 528. 關於法拉第
He was thus left at leisure to do his proper work, to coordinate his ideas with his facts, and to express them in natural untechnical language. 馬克斯威的說法 Treatise, Art. 528. 關於法拉第 leisure!
觀念的演進evolution of concepts force as action-at-a-distance 瞬時隔空作用 lines of force 場線 field of force 力場 Potential 勢
從「電」「磁」到「電磁」 安培 電流 電磁 磁場變化 法拉第
「電」「磁」 • Electric charges did not influence the magnets in any way; • Neither did the magnets influence the electric charges.
The honor of discovering the bridge between electricity and magnetism fell to a Danish physicist, Hans Christian Örsted.
Thus electromagnetism, as Örsted called it, became a reality! July 21, 1820
安培的想法及發現 不僅電流對磁針有作用， 電流對電流也會有作用。 Not only does an electric current act on magnetic needle but two electric currents act on one another.
